CN101706362A - Parameter calibration method of acousto-optic tunable filter - Google Patents

Abstract

The invention relates to a parameter calibration method of an acousto-optic tunable filter (AOTF). The calibration data of the wavelength response function, the wavelength frequency tuning relationship, the deflection angle beta, the wavelength relationship and the like of the AOTF are processed according to the principle of the AOTF, a method of combining a parameter theory expression and a least squares principle is adopted to inverse the internal parameters of the AOTF, and an approximation technology of an optical grating of an emergent face is adopted to realize the simulation of a light path of the AOTF. In the invention, the data processing method is novel, the accuracy of a processing result is higher, and the inversed internal parameters of the AOTF can provide an improved basis for the production of the AOTF and provide a light path tracking method for the optical design of a spectrograph of the AOTF.

Description

Parameter calibration method of acousto-optic tunable filter

Technical field

The present invention relates to a kind of acousto-optic tunable filter (Acousto-optic Tunable Filter, hereinafter to be referred as AOTF) parameter calibration method, incorporating parametric calibration data, accurate expression according to the AOTF parameter, carry out the AOTF parametric solution, be applicable to the index test of AOTF product, and utilize transmission grating approximate simulation AOTF beam split, for integrated AOTF spectrometer provides the optical design means, belong to hyperspectral imager calibration technology field.

Background technology

AOTF makes according to the acoustooptic diffraction principle, can rely on the variation of electric signal frequency to select wavelength, and wavelength X and frequency f satisfy the wavelength frequency tuning and concern f=f (λ).Spectrometer based on AOTF has characteristics such as miniature, gently little, able to programme, is used widely rapidly in the spectral analysis field.

AOTF is when making, and the machining deviation of ultrasonic off-axis angle and acoustic optic interaction makes index and design loads and inconsistent such as spectral resolution, wavelength frequency tuning relation and deflection angle.Therefore, after the making of finishing AOTF, its parameter calibrated help to find mismachining tolerance source to be of value to the improvement production technology.In addition, when optical design software such as utilizing ZMAX and Code V is carried out the design of AOTF spectrometer, can't find the optical element that to simulate AOTF, bring bigger trouble to optical design.

At present, both at home and abroad usually all be to the apparent parameter of AOTF for example angular aperture, wavelength frequency tuning relation etc. calibrate, and data processing method all is simple fitting of a polynomial; Simultaneously, though on the AOTF Parameters Calculation, carried out deep research both at home and abroad, but process all is the known internal parameter, spectral resolution, angular aperture and wavelength frequency tuning relation to AOTF are calculated, at present also not in conjunction with the calibration data, adopt accurate expression that inner parameter is carried out the reverse method of accurately finding the solution, therefore can't obtain inner parameter such as ultrasonic off-axis angle and the acousto-optic interaction length etc. of AOTF; Though proposed the scheme that grating replaces AOTF to carry out optical design abroad,, do not take all factors into consideration the variation of grating constant under different wave length and the incident angle in conjunction with the calibration data.

Summary of the invention

The object of the present invention is to provide a kind of parameter calibration method of acousto-optic tunable filter, only calibrate apparent parameter to overcome existing AOTF calibrating method, inner parameter can't be found the solution, shortcomings such as the approximate imperfection of grating, provide a kind of in conjunction with least square method and calibration data, utilization contains the method for the accurate expression calibration AOTF inside and outside parameter of acousto-optic crsytal optically-active parameter, and this method is resolved with grating at inner parameter has higher precision on approximate.

Technical solution of the present invention is: acousto-optic tunable filter (AOTF) parameter calibration method comprises the following steps:

(1) analyzes the principle of waiting to calibrate AOTF;

(2) determine the ordinary O optical index n of acousto-optic crsytal according to the ear plug G dispersion equation of acousto-optic crsytal _oWith extraordinary E optical index n _e

(3) determine the incident light refractive index n by acoustic optic interaction momentum matching condition and crystal refractive index ellipsoid _iWith the diffraction light refractive index n _dSize; Incident light is the O light time, n _i=n _o(θ _o), n _d=n _e(θ _e), incident light is the E light time, n _i=n _e(θ _e), n _d=n _o(θ _o), θ _oAnd θ _eBe respectively the angle of O light vector and the E light vector and the optical axis of crystal, n _o(θ _o) and n _e(θ _e) be respectively O light at θ _oThe refractive index of direction and E light are at θ _eThe refractive index of direction;

(4) determine ultrasonic vector and ultrasonic frequency size;

(5) determine light vector incident angle θ by the parallel tangents principle _iWith ultrasonic off-axis angle θ _aRelation:

θ _i=parallel (λ, θ _a), λ is a wavelength;

(6) utilize frequency f under the parallel tangents principle _iAnd wavelength X _iThe calibration data are according to the ultrasonic frequency function f _i=f (parallel (λ _i, θ _a), λ _i, θ _a), find the solution θ _a

Frequency f when (7) utilizing along the incident of acousto-optic tunable filter working-spindle direction _iAnd wavelength X _iThe calibration data are according to the ultrasonic frequency function f _i=f (θ _i, λ _i, θ _a), find the solution light vector incident angle θ _i, determine that the wavelength frequency tuning concerns f=f (θ _i, λ, θ _a);

(8) utilize the wavelength response function of AOTF to calibrate data, calculate half-peak value full bandwidth delta λ, and utilize spectral resolution

Find the solution the acoustic optic interaction length L, wherein b (λ) is the dispersion constant (DC) of acousto-optic crsytal;

(9) utilizing transmission grating that AOTF is carried out grating is similar to: d (λ) * (sin (θ _In) ± sin (θ _De))=λ, wherein θ _InAnd θ _DeBe respectively incident light and diffraction light and AOTF window normal angle, d (λ) is a grating constant to be found the solution, and is the function of wavelength; When incident light and diffraction light during at the normal homonymy, grating equation gets+, if heteropleural, then get-; θ _Inθ with different λ place _DeProvide by AOTF deflection angle calibration experiment.

Wherein, exact formulas is all adopted in the calculating of described ultrasonic vector of step (4) and ultrasonic frequency:

Wherein K is ultrasonic vector size, V (θ _a) be the θ that determines by crystal acoustics character _aThe ultrasonic velocity of direction, f is the ultrasonic frequency size, and has θ wherein _iBy the decision of incident light polarization direction, incident light is the O light time, θ _i=θ _o, incident light is the E light time, θ _i=θ _e

Step (6), step (7) and step (8) be described finds the solution ultrasonic off-axis angle θ _a, find the solution light vector incident angle θ _iAll adopt least square method with the method for finding the solution the acoustic optic interaction length L: promptly in feasible zone, seek θ _a, θ _iAnd L, make objective function respectively:

With

Minimalization, m wherein, n, o all are calibration data set number.

The described grating approximation method of step (9) obtains d (λ) by fitting of a polynomial, and the match factor is λ: by d (λ)=a ₀+ a ₁λ+a ₂λ ²+ ...+a _nλ ⁿGrating constant is carried out match, wherein a ₀, a ₁... a _nBe coefficient of polynomial fitting, n is the match exponent number, and the match factor is λ.

The AOTF parameter calibration system that used all kinds of calibration data utilization is made up of monochromatic line polarized light source, accurate automatically controlled turntable, optical power detector and high-precision radio frequency driving circuit in step (6), (7), (8) and (9) obtains.

Principle of the present invention is: the direction of ultrasonic vector is changeless with respect to the optical axis of crystal in the acousto-optic tunable filter (AOTF), in order to increase the acceptance angle of AOTF to incident light, usually with wave vector according to parallel tangents principle layout.But fixedly the time, only could satisfy the parallel tangents principle at light vector incident angle and ultrasonic vector angle under certain specific wavelength, this moment, wavelength frequency tuning relation was by f=f (θ _i, λ, θ _a) decision, because light vector incident angle θ in the formula _iWith ultrasonic off-axis angle θ _aIt all is unknown constant, can't utilize calibration data wavelength X and frequency f to solve. when passing through calibration, the present invention changes the light vector incident angle, obtain wavelength X and frequency f data under the parallel tangents principle, this moment, wavelength frequency tuning relation became f=f (parallel (λ, θ _a), λ, θ _a), single unknown quantity θ _aBecome and find the solution easily; To find the solution the θ that obtains again _aSubstitution f=f (θ _i, λ, θ _a) in, remaining unknown quantity θ _iAlso can ask; Finally, be fixed into firing angle θ _iThe wavelength frequency tuning concern f=f (θ _i, λ, θ _a) unique definite; The acoustic optic interaction length L can be tried to achieve by the expression formula and the calibration data of spectral resolution; Utilize many group calibration data, and utilize least square fitting, can improve the calibration precision of parameter significantly.AOTF is similar to ultrasonic grating on principle, utilize calibration data such as angle of incidence of light, angle of diffraction and branch optical wavelength, can be similar to according to the transmission grating equation, but the grating constant d that obtains (λ) can change along with wavelength change, the present invention is by the method for fitting of a polynomial, having obtained is d (λ) value of function with the wavelength, thereby can utilize grating to replace AOTF when optical design, reduces design difficulty.

The present invention's advantage compared with prior art is:

(1) according to the calibration data, utilizes the accurate expression that contains acousto-optic crsytal optically-active parameter, adopt least square method, the inner parameter of precise calibration AOTF.

(2) utilize transmission grating equation and in conjunction with deflection angle calibration data, AOTF is similar to, the grating constant multi-term expression of acquisition meets the dichroism under AOTF different wave length and the field angle.

Description of drawings

Fig. 1 is a theory diagram of the present invention;

Fig. 2 is the index ellipsoid of AOTF among the present invention;

Fig. 3 is the structure principle chart of AOTF among the present invention;

Fig. 4 is the structured flowchart of the AOTF parameter calibration system among the present invention.

Embodiment

As shown in Figure 1, 2, 3, the concrete grammar of calibration AOTF of the present invention is as follows:

(1) analyzes the principle of waiting to calibrate AOTF.AOTF mainly is made of acousto-optic crsytal (1) and transducer (2), as shown in Figure 3.The effect of transducer (2) is at intracrystalline ultrasound wave with electrical signal conversion, the length L of its length and acoustic optic interaction is relevant, ultrasound wave has the fixing direction of propagation in crystal, when satisfying wave vector momentum matching condition, incident light will produce Bragg diffraction, its diffraction light wavelength is corresponding one by one with the frequency of electric signal, changes the frequency of electric signal, just can change the diffraction light wavelength.

(2) according to AOTF usual acoustic luminescent crystal TeO ₂Birefringent characteristic, the refractive index n of its O light and E light _oAnd n _eEar plug G dispersion equation with wavelength variations is as follows:

${\mathrm{<figure-callout\; id="2"\; label="n\; o"\; filenames="H2009102415639E0000021.png,H2009102415639E0000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_o^{}=1+\frac{3.71789{\mathrm{\&lambda;}}^2}{{\mathrm{\&lambda;}}^2-{0.19619}^2}+\frac{0.07544{\mathrm{\&lambda;}}^2}{{\mathrm{\&lambda;}}^2-{4.61196}^2}$

${\mathrm{<figure-callout\; id="2"\; label="n\; e"\; filenames="H2009102415639E0000021.png,H2009102415639E0000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_e^{}=1+\frac{4.33449{\mathrm{\&lambda;}}^2}{{\mathrm{\&lambda;}}^2-{0.20242}^2}+\frac{0.14739{\mathrm{\&lambda;}}^2}{{\mathrm{\&lambda;}}^2-{4.93667}^2}$

Wherein, λ is an incident light wavelength in a vacuum.As shown in Figure 2, according to wave vector momentum matching condition, have:

$\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\stackrel{\&RightArrow;}{\mathrm{OB}}+\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\stackrel{\&RightArrow;}{\mathrm{BA}}=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\stackrel{\&RightArrow;}{\mathrm{OA}}$

Wherein

With

Be the refractive index vector,

With

Be respectively E light vector, ultrasonic vector and O light vector.

(3) determine the incident light refractive index n _iWith the diffraction light refractive index n _dSize.The refractive index vector

With

Terminal A and B satisfy the index ellipsoid equation:

$\frac{n_e^2\left({\mathrm{\&theta;}}_e\right){\cos }^2\left({\mathrm{\&theta;}}_e\right)}{n_o^2{(1+\mathrm{\&delta;})}^2}+\frac{n_e^2\left({\mathrm{\&theta;}}_e\right){\sin }^2\left({\mathrm{\&theta;}}_e\right)}{n_e^2}=1$ ①

$\frac{n_o^2\left({\mathrm{\&theta;}}_o\right){\cos }^2\left({\mathrm{\&theta;}}_o\right)}{n_o^2{(1-\mathrm{\&delta;})}^2}+\frac{n_o^2\left({\mathrm{\&theta;}}_o\right){\sin }^2\left({\mathrm{\&theta;}}_o\right)}{n_o^2}=1$

Wherein, δ is acousto-optic crsytal TeO ₂The optically-active parameter, θ _oAnd θ _eBe respectively the angle of O light vector and the E light vector and the optical axis of crystal, n _o(θ _o) be that O light is at θ _oThe refractive index of direction, n _e(θ _e) be that E light is at θ _eThe refractive index of direction; When incident light is the O light time, θ _oKnown, when incident light is the E light time, θ _eKnown.

(4) ultrasonic vector K (promptly

) the slope coordinate that can pass through vector terminal A, B determine, also be the angle theta of the ultrasonic vector and the optical axis of crystal simultaneously _aThe cotangent value, can get:

$\frac{n_e\left({\mathrm{\&theta;}}_e\right)\sin \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\sin \left({\mathrm{\&theta;}}_o\right)}{n_e\left({\mathrm{\&theta;}}_e\right)\cos \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\cos \left({\mathrm{\&theta;}}_o\right)}=\tan \left({\mathrm{\&theta;}}_a\right)$ ②

By solving an equation 1. and 2. can calculating n _o(θ _o), n _e(θ _e), θ _oOr θ _eValue, finally determine the coordinate figure of A, B.

Ultrasonic vector K (promptly

) the Euclidean distance of big I by A, B coordinate provide:

$K=\frac{2\mathrm{\&pi;f}}{V\left({\mathrm{\&theta;}}_a\right)}=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{{(n_e\left({\mathrm{\&theta;}}_e\right)\sin \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\sin \left({\mathrm{\&theta;}}_o\right))}^2+{(n_e\left({\mathrm{\&theta;}}_e\right)\cos \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\cos \left({\mathrm{\&theta;}}_o\right))}^2}$

Wherein, K is ultrasonic vector size, V (θ _a) be that ultrasound wave is along θ _aSpeed, can calculate by crystal acoustics character, f is the ultrasonic frequency size.Then the wavelength frequency tuning of AOTF closes and is:

$f({\mathrm{\&theta;}}_i,\mathrm{\&lambda;},{\mathrm{\&theta;}}_a)=\frac{V\left({\mathrm{\&theta;}}_a\right)}{\mathrm{\&lambda;}}\sqrt{{(n_e\left({\mathrm{\&theta;}}_e\right)\sin \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\sin \left({\mathrm{\&theta;}}_o\right))}^2+{(n_e\left({\mathrm{\&theta;}}_e\right)\cos \left({\mathrm{\&theta;}}_e\right)-n_o\left({\mathrm{\&theta;}}_o\right)\cos \left({\mathrm{\&theta;}}_o\right))}^2}$

③

The θ in equal sign left side wherein _iBy the decision of incident light polarization direction, incident light is the O light time, θ _i=θ _o, incident light is the E light time, θ _i=θ _eAs seen, the incident angle θ of determining _iWith off-axis angle θ _aDown, the driving frequency of AOTF is the function of branch optical wavelength, and relation is one to one arranged.

(5) AOTF often adopts parallel tangents vector layout in order to increase the angle that receives light, and promptly O light ellipsoid and E light ellipsoid are crossed two tangent lines that A point and B order respectively and be parallel to each other, and have at this moment:

$n_e^2{(1-\mathrm{\&delta;})}^2\tan {\mathrm{\&theta;}}_o=n_o^2{(1+\mathrm{\&delta;})}^2\tan {\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="4"\; label="e"\; filenames="H2009102415639E0000022.png"\; state="\{\{state\}\}">e</figure-callout>}}$ ④

To 2. formula of 4. formula substitution, can obtain θ _oAnd θ _eAbout θ _aEquation, incident angle θ _iLook the incident polarization direction and can be taken as θ _oPerhaps θ _e, θ then _iBe θ _aFunction, be designated as:

θ _i＝parallel(λ，θ _a) ⑤

(6) 3., then can determine the wavelength tuning function under the parallel tangents principle, this moment, the driving frequency of AOTF only was the function of branch optical wavelength and ultrasonic off-axis angle, was designated as with 5. substitution formula of formula:

f＝f(parallel(λ，θ _a)，λ，θ _a) ⑥

As seen, as long as known the calibration data of wavelength and frequency under the parallel tangents principle, obtain ultrasonic off-axis angle θ with regard to available formula is 6. counter _aBy mathematical meaning, under same wavelength and the ultrasonic off-axis angle, when satisfying the parallel tangents principle, ultrasonic frequency is got minimum point with respect to the light vector under other angle incident:

f(parallel(λ，θ _a)，λ，θ _a)＝min(f(θ _i，λ，θ _a))； ${\mathrm{\&theta;}}_i\&Element;(-\frac{\mathrm{\&pi;}}{2},\frac{\mathrm{\&pi;}}{2})$ ⑦

By 7. formula, be the incident light of λ to wavelength, measure the minimum frequency values of AOTF under different light vector incident angles, promptly get the wavelength X that satisfies the parallel tangents principle _iAnd frequency f _iThe calibration data.If the calibration data that record have m group, according to least square method, feasible zone (0, seek θ in π) _a, make objective function

Reach minimal value, can effectively utilize the calibration data thus, improve calculation accuracy.

When (7) AOTF used as the light-splitting device of spectrometer, the optical axis of optical system was the working-spindle direction of AOTF.The frequency f that utilization is calibrated during along the incident of AOTF working-spindle direction _iAnd wavelength X _iData are according to the ultrasonic frequency function f _i=f (θ _i, λ _i, θ _a), find the solution light vector incident angle θ _i, determine that the wavelength frequency tuning concerns f=f (θ _i, λ, θ _a).If the calibration data that record have the n group, according to least square method, at feasible zone

The interior θ that seeks _i, make objective function

Reach minimal value, θ in the formula _aBe the ultrasonic off-axis angle value of calibrating under the parallel tangents principle.

(8) the wavelength response function is a central wavelength lambda _iThe AOTF of place is to the response efficiency of each wavelength in the service band, and its centre frequency corresponds to f _i=f (parallel (λ _i, θ _a), λ _i, θ _a), the light vector incident angle is θ _i=parallel (λ _i, θ _a).According to wavelength response function calibration data, calculate half-peak value full bandwidth delta λ, and utilize the spectral resolution formula Utilize least square method, in feasible zone, seek L, make objective function

Minimalization, wherein o is calibration data set number, b (λ) is the dispersion constant (DC) of acousto-optic crsytal.

(9) the transmission grating equation is d (λ) * (sin (θ _In) ± sin (θ _De))=λ, wherein θ _InAnd θ _DeBe respectively incident light and diffraction light and AOTF window normal angle, can be provided by AOTF deflection angle calibration experiment, d (λ) is a grating constant to be found the solution, be the function of wavelength, when incident light and diffraction light during at the normal homonymy, grating equation gets+number, if heteropleural, then get-number.Utilize different wave length λ _iThe θ at place _InAnd θ _DeThe calibration data are found the solution d (λ _i) value, and be independent variable with λ, by polynomial expression d (λ)=a ₀+ a ₁λ+a ₂λ ²+ ...+a _nλ ⁿGrating constant is carried out match, wherein a ₀, a ₁... a _nBe fitting coefficient, n is the match exponent number.

As shown in Figure 4, AOTF parameter calibration system among the present invention is made up of monochromatic line polarized light source 1, accurate automatically controlled turntable 2, optical power detector 3 and high-precision radio frequency driving circuit 4, high-precision radio frequency driving circuit 4 output frequencies are accurate, the signal of power stability drives AOTF, make AOTF produce diffraction to the emergent light of monochromatic line polarized light source 1, diffraction light that obtains and AOTF window normal angle are θ _DeUnder fixing wavelength and ultrasonic off-axis angle, when satisfying the parallel tangents principle, ultrasonic frequency is got minimal value with respect to the light vector under other angle incident, control accurate automatically controlled turntable 2 rotations, obtain the minimal value of ultrasonic frequency when momentum mates under the different incidence angles, be the wavelength X that satisfies the parallel tangents principle _iAnd frequency f _iThe calibration data; The automatically controlled turntable 2 of precision is rotated to the working-spindle direction, measure the ultrasonic frequency value when momentum mates under the different wave length, the frequency f when being along the incident of AOTF working-spindle direction _iAnd wavelength X _iThe calibration data; Fixed drive frequency utilizes optical power detector 3 to measure diffraction light power and incident optical power under the different wave length respectively, and both ratios are wavelength response function calibration data with the curve of wavelength variations; Control accurate automatically controlled turntable 2, making incident light AOTF window normal angle is θ _In, measure diffraction light and AOTF normal angle value θ under the different wave length _DeBe deflection angle calibration data.

Claims (4)

1. parameter calibration method of acousto-optic tunable filter is characterized in that comprising the following steps:

(1) analyzes the principle of waiting to calibrate acousto-optic tunable filter;

(2) determine the ordinary O optical index n of acousto-optic crsytal according to the ear plug G dispersion equation of acousto-optic crsytal _oWith extraordinary E optical index n _e

(3) determine the incident light refractive index n by acoustic optic interaction momentum matching condition and crystal refractive index ellipsoid _iWith the diffraction light refractive index n _dSize, incident light are the O light time, n _i=n _o(θ _o), n _d=n _e(θ _e), incident light is the E light time, n _i=n _e(θ _e), n _d=n _o(θ _o), θ _oAnd θ _eBe respectively the angle of O light vector and the E light vector and the optical axis of crystal, n _o(θ _o) and n _e(θ _e) be respectively O light at θ _oThe refractive index of direction and E light are at θ _eThe refractive index of direction;

(4) determine ultrasonic vector and ultrasonic frequency size;

(5) determine light vector incident angle θ by the parallel tangents principle _iWith ultrasonic off-axis angle θ _aRelation: θ _i=parallel (λ, θ _a), λ is a wavelength;

(6) utilize frequency f under the parallel tangents principle _iAnd wavelength X _iThe calibration data are according to the ultrasonic frequency function f _i=f (parallel (λ _i, θ _a), λ _i, θ _a), find the solution θ _a

Frequency f when (7) utilizing along the incident of acousto-optic tunable filter working-spindle direction _iAnd wavelength X _iThe calibration data are according to the ultrasonic frequency function f _i=f (θ _i, λ _i, θ _a), find the solution light vector incident angle θ _i, determine that the wavelength frequency tuning concerns f=f (θ _i, λ, θ _a);

(8) utilize the wavelength response function of acousto-optic tunable filter to calibrate data, calculate half-peak value full bandwidth delta λ, and utilize spectral resolution

Find the solution the acoustic optic interaction length L, wherein b (λ) is the dispersion constant (DC) of acousto-optic crsytal;

(9) utilizing transmission grating that acousto-optic tunable filter is carried out grating is similar to: d (λ) * (sin (θ _In) ± sin (θ _De))=λ, wherein θ _InAnd θ _DeBe respectively incident light and diffraction light and acousto-optic tunable filter window normal angle, d (λ) is a grating constant to be found the solution, and is the function of wavelength; When incident light and diffraction light during at the normal homonymy, grating equation gets+, if heteropleural, then get-; θ _Inθ with different λ place _DeProvide by acousto-optic tunable filter deflection angle calibration experiment.

2. parameter calibration method of acousto-optic tunable filter according to claim 1 is characterized in that: described step (4) adopts exact formulas when calculating ultrasonic vector and ultrasonic frequency size,

Wherein K is ultrasonic vector size, V (θ _a) be the θ that determines by crystal acoustics character _aThe ultrasonic velocity of direction, f is the ultrasonic frequency size, and has

θ wherein _iBy the decision of incident light polarization direction, incident light is the O light time, θ _i=θ _o, incident light is the E light time, θ _i=θ _e

3. parameter calibration method of acousto-optic tunable filter according to claim 1 is characterized in that: described step (6) θ _aFind the solution, step (7) θ _iFind the solution and step (8) L method for solving all adopts least square method, promptly in feasible zone, seek θ _a, θ _iAnd L, make objective function respectively:

With

Minimalization, m wherein, n, o all are calibration data set number.

4. parameter calibration method of acousto-optic tunable filter according to claim 1 is characterized in that: described step (9) grating approximation method is by d (λ)=a ₀+ a ₁λ+a ₂λ ²+ ...+a _nλ ⁿGrating constant is carried out match, wherein θ ₀, a ₁... a _nBe coefficient of polynomial fitting, n is the match exponent number, and the match factor is λ.

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